1. Field of the Invention
The present invention relates to an image display using a delta arrangement type screen. This is suitable for driving a flat panel display.
Visual media including television broadcasting and various types of video disks have been becoming a high resolution. As the development of them, an image display apparatus having high quality and a large screen is desired to be available for an inexpensive price.
2. Description of the Prior Art
An image display apparatus using a plasma display panel has an input interface for receiving a signal from an image output device such as a television tuner or a computer, as a previous stage of a driving circuit that applies a voltage for generating discharge to the plasma display panel. The input interface converts an analog image signal to digital image data, and it sends image data with gamma correction to the driving circuit.
In general, a pixel arrangement of an image that is supplied to the image display apparatus is an orthogonal arrangement (or a tetragonal arrangement). Namely, the input image signal is prepared on the precondition of a display using an orthogonal arrangement type screen having cells aligned in a row and in a column of a matrix display. Here, the orthogonal arrangement type includes one whose pixel does not have an orthogonal shape. It is not necessary that a pitch of rows is identical to a pitch of columns.
In an image display apparatus having an orthogonal arrangement type screen, resolution conversion is performed for adjusting a resolution of an input image to a resolution of the display screen. The conversion of resolution in the horizontal direction (the conversion of the number of dots) is realized by adjusting a timing of a sampling clock while converting the analog image signal to the digital image data. The conversion of resolution in the vertical direction (the conversion of the number of rows) is realized by an interpolation process in accordance with data of plural lines (rows). The number of rows can be doubled by generating a new row of data from a mean value of data of two neighboring rows and inserting the new row between the original two rows. Also, the number of rows can be reduced to a half by replacing the original two rows with the newly generated row.
On the other hand, concerning a screen structure of a flat panel display, a plasma display panel having a delta arrangement type screen is disclosed in Japanese unexamined patent publication No. 9-50768. Here, the delta arrangement means one of arrangement formats of cells that are display elements constituting a screen, in which a position of a cell is shifted between neighboring columns of cells by a half pitch. The half pitch means a half of a cell pitch between columns. A color display has pixels each of which is made of a set of red, green and blue cells. Therefore, noting one of the three colors, a center position of light emission of a pixel is shifted between neighboring columns of pixels by a half pitch in the delta arrangement. The delta arrangement in a plasma display panel has an advantage that an aperture can be larger than in the orthogonal arrangement, and it is an arrangement format that is suitable for improving luminance and light emission efficiency. Hereinafter, a plasma display panel having a delta arrangement type screen is referred to as a delta panel.
It is necessary to perform an image process that is called an arrangement conversion in a display using a delta panel. The arrangement conversion is a process for converting an orthogonal arrangement image to be displayed into an image that is adapted to the cell arrangement of the display screen. More specifically, it is an operation for distributing pixel values of the image to cells of the screen, so as to compensate the displacement between the pixel position of the image and the cell position of the screen. Japanese unexamined patent publication No. 2003-122293 discloses an image display apparatus having a conversion circuit that performs an add operation with weighting for the arrangement conversion and is disposed between the input interface and the driving circuit.
In a display apparatus having a screen in which a finite number of pixels are arranged in a discrete manner regardless of an arrangement format of pixels, a false frequency component that is called aliasing appears in an image to be displayed. In the orthogonal arrangement screen that is shown in FIG. 1 schematically, the aliasing as shown in FIGS. 2 and 3 appears. The image can be reproduced faithfully only in an area that is a vicinity of a spectrum center of the original signal. A boundary between areas in which faithful reproduction is possible and impossible in the frequency space is a Nyquist limit. The Nyquist limit in the orthogonal arrangement forms a quadrangle as shown in FIG. 2. As shown well in FIG. 3, the Nyquist limit is located at the middle position between the spectrum center of the original signal and the spectrum center of the aliasing that is adjacent to the spectrum of the original signal. When trying to display an image having a frequency component above the Nyquist limit, the image cannot be reproduced faithfully since it is overlapped with a component of the aliasing. Therefore, low-pass filtering is performed so that frequency components of the image signal in the horizontal direction and in the vertical direction are restricted within the Nyquist limit when displaying the image using an orthogonal arrangement type screen.
In general, a filtering process in a display apparatus utilizes an image filter of a neighborhood operation type for calculating luminance of a pixel in the screen by an add operation with weighting from luminance of plural data points in the input image. It is because that the image filter of such a type enables a higher speed of process than a Fourier transform type and is suitable for a display of a moving picture.
There is a problem in the conventional image display apparatus having the delta arrangement type screen. The problem is that a part of the input image signal having a high space frequency is replaced with a false signal and is overlapped with information having a low space frequency that must be inherently displayable; thereby the image information of the part is dropped out completely in the display.
The problem that a part of the input image signal is replaced with a false signal can be solved by making the screen high definition so as to enlarge the space frequency area that can be displayed. However, this solution may cause a significant rise of cost of the image display apparatus.
Detail of the false signal is as follows. In a display using a delta arrangement screen that is shown in FIG. 4 schematically, the aliasing as shown in FIG. 5 appears. Since the arrangement of the spectrum center of the aliasing in the frequency space also becomes the delta arrangement, a shape of the Nyquist limit becomes a hexagon as a characteristic of the delta arrangement screen. Therefore, in order to realize reproduction of a faithful image, band limitation in a “diagonal direction” that is a slanting direction to the vertical direction and the horizontal direction is necessary adding to the band limitation in the vertical direction and in the horizontal direction. However, in the conventional method only the band limitation in the vertical direction and in the horizontal direction is performed in the same way as the orthogonal arrangement, and the band limitation in the diagonal direction is not performed. Thus, in a display apparatus having a delta arrangement type screen, the band limitation in the diagonal direction using an image filter is not realized for the purpose of reproducing an image faithfully.
Although it is not aimed at the band limitation, a sort of operation for converting the orthogonal arrangement format of an image signal into the delta arrangement format corresponds to the filtering in the diagonal direction. The operation is a neighborhood operation (sometimes called a filter matrix operation) in which pixel information of the input image is distributed not only to the pixels in the vertical direction but also to pixels in the horizontal direction. The operation will be explained more specifically as below.
First, symbols are prepared. A gradation level of a cell of a color is denoted by Cn,m, and an image signal that corresponds to a cell of a noted color is denoted by Tn,m. The suffix “n” means a position in the vertical direction, while the suffix “m” means a position in the horizontal direction. These positions are defined as shown in FIGS. 6 and 7. Here, it should be noted that numbering of the position is different depending on a color. The position of the even cell in the horizontal direction is shifted from the position of the odd cell by a half of the cell pitch in the vertical direction.
Concerning the vertical position of a horizontal line (row) of the image signal, there are two cases supposed; one is the case (a type A) where it is the same position as the cell as shown in FIG. 8, and another is the case (a type B) where it is the middle position between the neighboring cells.
The neighborhood operation for the conventional format conversion is an operation to an interlace signal having double numbers of horizontal lines of the screen. Hereinafter, interlace image information is denoted by T′n,m, information of even field is denoted by T′2n,m, and information of odd field is denoted by T′2n+1,m. The operation is expressed by the following expressions.
                    [                  For          ⁢                                          ⁢          an          ⁢                                          ⁢          even          ⁢                                          ⁢          field          ⁢                                          ⁢          in          ⁢                                          ⁢          the          ⁢                                          ⁢          type          ⁢                                          ⁢          A                ]                                                                                                                                                      C                                                                  2                        ⁢                        n                                            ,                                              2                        ⁢                        m                                                                              =                                                                                    1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                  15                        16                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                                                                                                                                                      C                                                                                            2                          ⁢                          n                                                +                        1                                            ,                                                                        2                          ⁢                          m                                                +                        1                                                                              =                                                                                    1                        64                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  15                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    1                        64                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                              +                                                                  1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            2                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    15                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            2                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            2                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                                                                                          }                ⁢                                  ⁢                                                            (                                  R                  ⁢                                                                          ⁢                  and                  ⁢                                                                          ⁢                  B                                                                                                        cells                )                                                                        (        1        )                                                                                                                          C                                                                  2                        ⁢                        n                                            ,                                                                        2                          ⁢                          m                                                +                        1                                                                              =                                                                                    1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  15                        16                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                                                                                                                                                      C                                                                                            2                          ⁢                          n                                                +                        1                                            ,                                              2                        ⁢                        m                                                                              =                                                                                    1                        64                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                  15                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    1                        64                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            2                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    15                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            2                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            2                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                                                                                          }                ⁢                                  ⁢                  (                      G            ⁢                                                  ⁢            cell                    )                                    (        2        )                                [                  For          ⁢                                          ⁢          an          ⁢                                          ⁢          odd          ⁢                                          ⁢          field          ⁢                                          ⁢          in          ⁢                                          ⁢          the          ⁢                                          ⁢          type          ⁢                                          ⁢          A                ]                                                                                                                                                      C                                                                  2                        ⁢                        n                                            ,                                              2                        ⁢                        m                                                                              =                                                                                    1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                  15                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                  15                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                                                                                                                                                      C                                                                                            2                          ⁢                          n                                                +                        1                                            ,                                                                        2                          ⁢                          m                                                +                        1                                                                              =                                                                                    1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  15                        16                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                            1                      32                                        ⁢                                          T                                                                                                    2                            ⁢                            n                                                    +                          1                                                ,                                                                              2                            ⁢                            m                                                    +                          2                                                                    ′                                                                                                    }                ⁢                                  ⁢                                                            (                R                                                                        and                                                          B                                                                          cells                )                                                                        (        3        )                                                                                                                          C                                                                  2                        ⁢                        n                                            ,                                                                        2                          ⁢                          m                                                +                        1                                                                              =                                                                                    1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  15                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                              +                                                                  1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    15                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  1                        64                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                                                                                                                                                      C                                                                                            2                          ⁢                          n                                                +                        1                                            ,                                              2                        ⁢                        m                                                                              =                                                                                    1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                  15                        16                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                                                                                          }                ⁢                                  ⁢                                                            (                G                                                                                        cell                )                                                                        (        4        )                                [                  For          ⁢                                          ⁢          an          ⁢                                          ⁢          even          ⁢                                          ⁢          field          ⁢                                          ⁢          in          ⁢                                          ⁢          the          ⁢                                          ⁢          type          ⁢                                          ⁢          B                ]                                                                                                                                                      C                                                                  2                        ⁢                        n                                            ,                                              2                        ⁢                        m                                                                              =                                                                                    7                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            2                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    23                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                                                                                                                                                      C                                                                                            2                          ⁢                          n                                                +                        1                                            ,                                                                        2                          ⁢                          m                                                +                        1                                                                              =                                                                                    1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  23                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                              +                                                                  7                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            2                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                                                                                          }                ⁢                                  ⁢                                                            (                                  R                  ⁢                                                                          ⁢                  and                  ⁢                                                                          ⁢                  B                                                                                                        cells                )                                                                        (        5        )                                                                                                                          C                                                                  2                        ⁢                        n                                            ,                                                                        2                          ⁢                          m                                                +                        1                                                                              =                                                                                    7                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            2                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    23                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                                                                                                                                                      C                                                                                            2                          ⁢                          n                                                +                        1                                            ,                                              2                        ⁢                        m                                                                              =                                                                                    1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                  23                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    1                        32                                            ⁢                                              T                                                                              2                            ⁢                            n                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  7                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            2                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                                                                                          }                ⁢                                  ⁢                  (                      G            ⁢                                                  ⁢            cell                    )                                    (        6        )                                [                  For          ⁢                                          ⁢          an          ⁢                                          ⁢          odd          ⁢                                          ⁢          field          ⁢                                          ⁢          in          ⁢                                          ⁢          the          ⁢                                          ⁢          type          ⁢                                          ⁢          B                ]                                                                                                                                                      C                                                                  2                        ⁢                        n                                            ,                                              2                        ⁢                        m                                                                              =                                                                                    1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                  23                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  7                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                                                                                                                                                      C                                                                                            2                          ⁢                          n                                                +                        1                                            ,                                                                        2                          ⁢                          m                                                +                        1                                                                              =                                                                                    7                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    23                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                                                                                          }                ⁢                                  ⁢                                                            (                                  R                  ⁢                                                                          ⁢                  and                  ⁢                                                                          ⁢                  B                                                                                                        cells                )                                                                        (        7        )                                                                                                                          C                                                                  2                        ⁢                        n                                            ,                                                                        2                          ⁢                          m                                                +                        1                                                                              =                                                                                    1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  23                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            2                                                                          ′                                                              +                                                                  7                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                                                                                                                                                      C                                                                                            2                          ⁢                          n                                                +                        1                                            ,                                              2                        ⁢                        m                                                                              =                                                                                    7                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        -                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        -                            1                                                                          ′                                                              +                                                                                                                                                                                ⁢                                                                                    23                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                      2                            ⁢                            m                                                                          ′                                                              +                                                                  1                        32                                            ⁢                                              T                                                                                                            2                              ⁢                              n                                                        +                            1                                                    ,                                                                                    2                              ⁢                              m                                                        +                            1                                                                          ′                                                                                                                          }                ⁢                                  ⁢                  (                      G            ⁢                                                  ⁢            cell                    )                                    (        8        )            
Further, averaging between the even field and the odd field, the above operations become as follows. The operation expression is common to three colors of red, green and blue. However, suffixes should be considered.
                    [                  Type          ⁢                                          ⁢          A                ]                                                                      C                      n            ,            m                          =                                            1              128                        ⁢                          T                                                n                  -                  1                                ,                                  m                  -                  1                                            ′                                +                                    15              64                        ⁢                          T                                                n                  -                  1                                ,                m                            ′                                +                                    1              128                        ⁢                          T                                                n                  -                  1                                ,                                  m                  +                  1                                            ′                                +                                    (        9        )                                                          ⁢                                            1              64                        ⁢                          T                              n                ,                                  m                  -                  1                                            ′                                +                                    15              32                        ⁢                          T                              n                ,                m                            ′                                +                                    1              64                        ⁢                          T                              n                ,                                  m                  +                  1                                            ′                                +                                                                                              ⁢                                            1              128                        ⁢                          T                                                n                  +                  1                                ,                                  m                  -                  1                                            ′                                +                                    15              64                        ⁢                          T                                                n                  +                  1                                ,                m                            ′                                +                                    1              128                        ⁢                          T                                                n                  +                  1                                ,                                  m                  +                  1                                            ′                                                                                          [                  Type          ⁢                                          ⁢          B                ]                                                                      C                      n            ,            m                          =                                            7              64                        ⁢                          T                                                n                  -                  2                                ,                m                            ′                                +                                    1              64                        ⁢                          T                                                n                  -                  1                                ,                                  m                  -                  1                                            ′                                +                                    23              64                        ⁢                          T                                                n                  -                  1                                ,                m                            ′                                +                                    1              64                        ⁢                          T                                                n                  -                  1                                ,                                  m                  +                  1                                            ′                                +                                    (        10        )                                                          ⁢                                            1              64                        ⁢                          T                              n                ,                                  m                  -                  1                                            ′                                +                                    23              64                        ⁢                          T                              n                ,                m                            ′                                +                                    1              64                        ⁢                          T                              n                ,                                  m                  +                  1                                            ′                                +                                    7              64                        ⁢                          T                                                n                  +                  1                                ,                                  m                  -                  1                                            ′                                                                      
These operations for the format conversion works also as low pass filters but are not designed as low pass filters. Therefore, they don't provide characteristics of band limitation filters that are adapted to the delta arrangement screen.